Using several cosmological observations, i.e. the cosmic microwave background anisotropies (WMAP), the weak gravitational lensing (CFHTLS), the measurements of baryon acoustic oscillations (SDSS+WiggleZ), the most recent observational Hubble parameter data, the Union2.1 compilation of type Ia supernovae, and the HST prior, we impose constraints on the sum of neutrino masses (Sigma m(v)), the effective number of neutrino species (N-eff) and dark energy equation of state (w), individually and collectively. We find that a tight upper limit on Sigma m(v) can be extracted from the full data combination, if N-eff and w are fixed. However this upper bound is severely weakened if N-eff and w are allowed to vary. This result naturally raises questions on the robustness of previous strict upper bounds on Sigma m(v), ever reported in the literature. The best-fit values from our most generalized constraint read Sigma m(v) = 0.556(-0.288)(+0.231) eV, N-eff = 3.839 +/- 0.452, and w = -1.058 +/- 0.088 at 68% confidence level, which shows a firm lower limit on total neutrino mass, favors an extra light degree of freedom, and supports the cosmological constant model. The current weak lensing data are already helpful in constraining cosmological model parameters for fixed w. The dataset of Hubble parameter gains numerous advantages over supernovae when w = -1, particularly its illuminating power in constraining N-eff. As long as w is included as a free parameter, it is still the standardizable candles of type Ia supernovae that play the most dominant role in the parameter constraints.

NASA Office of Space Science; National Science Foundation of China [11173006]; Ministry of Science and Technology National Basic Science program (project 973) [2012CB821804]; Fundamental Research Funds for the Central Universities; Natural Science Foundation of China [11033002]; National Basic Research Program of China (973 Program) [2009CB824800]
; NASA Office of Space Science; National Science Foundation of China [11173006]; Ministry of Science and Technology National Basic Science program (project 973) [2012CB821804]; Fundamental Research Funds for the Central Universities; Natural Science Foundation of China [11033002]; National Basic Research Program of China (973 Program) [2009CB824800]
; NASA Office of Space Science; National Science Foundation of China [11173006]; Ministry of Science and Technology National Basic Science program (project 973) [2012CB821804]; Fundamental Research Funds for the Central Universities; Natural Science Foundation of China [11033002]; National Basic Research Program of China (973 Program) [2009CB824800]
; NASA Office of Space Science; National Science Foundation of China [11173006]; Ministry of Science and Technology National Basic Science program (project 973) [2012CB821804]; Fundamental Research Funds for the Central Universities; Natural Science Foundation of China [11033002]; National Basic Research Program of China (973 Program) [2009CB824800]